Analog Gravity in Magneto-Viscous Fluids: Enhanced Analog Hawking Temperature in Accretion Disks
We present a three-dimensional visco-magnetoacoustic framework for analog gravity in magnetohydrodynamic (MHD) flows. While standard fluid dissipation typically breaks the Lorentzian signature of acoustic metrics, we demonstrate that evaluating wave perturbations in the eikonal limit alongside the Shakura-Sunyaev $α$-viscosity prescription preserves a well-defined effective spacetime geometry for the fast magnetoacoustic mode. The slow-magnetoacoustic mode and Alfvén mode do not admit a non-degenerate metric. To investigate analog horizon thermodynamics, we utilize astrophysical accretion disks as background media, specifically modeling numerical magnetized advective accretion flows around rotating black holes and analytical advection-dominated inflow-outflow solutions (ADIOS). Standard self-similar ADIOS models strictly enforce a constant Mach number, precluding horizon formation. We therefore introduce a magnetic field perturbation that breaks self-similarity, generates a dynamic Mach number, and enables the formation of a visco-magnetoacoustic horizon. By evaluating the spontaneous phonon emission at these horizons, we reveal that the analog Hawking temperature is highly sensitive to the magnetic field topology; the spatial orientation of the background magnetic gradients dictates whether the Hawking radiation is amplified or suppressed. Furthermore, we find that increasing the viscosity parameter leads to a monotonic increase in the analog Hawking temperature.